Properties

Label 4592.l
Number of curves $2$
Conductor $4592$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4592.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4592.l1 4592f2 [0, 0, 0, -153781003, 734010288314] [] 592704  
4592.l2 4592f1 [0, 0, 0, -309643, -61048006] [] 84672 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4592.l have rank \(0\).

Complex multiplication

The elliptic curves in class 4592.l do not have complex multiplication.

Modular form 4592.2.a.l

sage: E.q_eigenform(10)
 
\( q + 3q^{3} - q^{5} - q^{7} + 6q^{9} + 2q^{11} - 3q^{15} - 3q^{17} + 8q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.